The nature of $σ$, $κ$, $a_0(980)$ and $f_0(980)$

Details The nature of $σ$, $κ$, $a_0(980)$ and $f_0(980)$ The nature of $σ$, $κ$, $a_0(980)$ and $f_0(980)$

2006-06-01

arxiv.org/abs/hep-ph/0606022v2

Phys.Lett.B641:265-271,2006

Physics

High Energy Physics

High Energy Physics - Phenomenology

Plain LaTeX, 10 pages, 3 EPS figures; v2: 11 pages, better-quality figures, extra references, version accepted for publication

Scientific paper

10.1016/j.physletb.2006.08.051

Masses and widths of the four light scalar mesons $\sigma$, $\kappa$, $a_0$(980) and $f_0$(980) may be reproduced in a model where mesons scatter via a $q\bar{q}$ loop. A transition potential is used to couple mesons to $q\bar{q}$ at a radius of $\sim 0.57$ fm. Inside this radius, there is an infinite bare spectrum of confined $q\bar{q}$ states, for which a harmonic oscillator is chosen here. The coupled-channel system approximately reproduces the features of both light and heavy meson spectroscopy. The generation of $\sigma$, $\kappa$, $a_0(980)$ and $f_0(980)$ is a balance between attraction due to the $q\bar q$ loop and suppression of the amplitudes at the Adler zeros. Phase shifts increase more rapidly as the coupling constant to the mesons increases. This leads to resonant widths which decrease with increasing coupling constant - a characteristically non-perturbative effect.

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